151 research outputs found
Bulk and Boundary Critical Behavior at Lifshitz Points
Lifshitz points are multicritical points at which a disordered phase, a
homogeneous ordered phase, and a modulated ordered phase meet. Their bulk
universality classes are described by natural generalizations of the standard
model. Analyzing these models systematically via modern
field-theoretic renormalization group methods has been a long-standing
challenge ever since their introduction in the middle of the 1970s. We survey
the recent progress made in this direction, discussing results obtained via
dimensionality expansions, how they compare with Monte Carlo results, and open
problems. These advances opened the way towards systematic studies of boundary
critical behavior at -axial Lifshitz points. The possible boundary critical
behavior depends on whether the surface plane is perpendicular to one of the
modulation axes or parallel to all of them. We show that the semi-infinite
field theories representing the corresponding surface universality classes in
these two cases of perpendicular and parallel surface orientation differ
crucially in their Hamiltonian's boundary terms and the implied boundary
conditions, and explain recent results along with our current understanding of
this matter.Comment: Invited contribution to STATPHYS 22, to be published in the
Proceedings of the 22nd International Conference on Statistical Physics
(STATPHYS 22) of the International Union of Pure and Applied Physics (IUPAP),
4--9 July 2004, Bangalore, Indi
Specific heat amplitude ratios for anisotropic Lifshitz critical behaviors
We determine the specific heat amplitude ratio near a -axial Lifshitz
point and show its universal character. Using a recent renormalization group
picture along with new field-theoretical -expansion techniques,
we established this amplitude ratio at one-loop order. We estimate the
numerical value of this amplitude ratio for and . The result is in
very good agreement with its experimental measurement on the magnetic material
. It is shown that in the limit it trivially reduces to the
Ising-like amplitude ratio.Comment: 8 pages, RevTex, accepted as a Brief Report in Physical Review
Statistical mechanics of double-stranded semi-flexible polymers
We study the statistical mechanics of double-stranded semi-flexible polymers
using both analytical techniques and simulation. We find a transition at some
finite temperature, from a type of short range order to a fundamentally
different sort of short range order. In the high temperature regime, the
2-point correlation functions of the object are identical to worm-like chains,
while in the low temperature regime they are different due to a twist
structure. In the low temperature phase, the polymers develop a kink-rod
structure which could clarify some recent puzzling experiments on actin.Comment: 4 pages, 3 figures; final version for publication - slight
modifications to text and figure
A new picture of the Lifshitz critical behavior
New field theoretic renormalization group methods are developed to describe
in a unified fashion the critical exponents of an m-fold Lifshitz point at the
two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close
to 8) situations. The general theory is illustrated for the N-vector phi^4
model describing a d-dimensional system. A new regularization and
renormalization procedure is presented for both types of Lifshitz behavior. The
anisotropic cases are formulated with two independent renormalization group
transformations. The description of the isotropic behavior requires only one
type of renormalization group transformation. We point out the conceptual
advantages implicit in this picture and show how this framework is related to
other previous renormalization group treatments for the Lifshitz problem. The
Feynman diagrams of arbitrary loop-order can be performed analytically provided
these integrals are considered to be homogeneous functions of the external
momenta scales. The anisotropic universality class (N,d,m) reduces easily to
the Ising-like (N,d) when m=0. We show that the isotropic universality class
(N,m) when m is close to 8 cannot be obtained from the anisotropic one in the
limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in
good agreement with recent Monte Carlo simulations for the ANNNI model.Comment: 48 pages, no figures, two typos fixe
Compatibility of 1/n and epsilon expansions for critical exponents at m-axial Lifshitz points
The critical behaviour of d-dimensional n-vector models at m-axial Lifshitz
points is considered for general values of m in the large-n limit. It is proven
that the recently obtained large-N expansions [J. Phys.: Condens. Matter 17,
S1947 (2005)] of the correlation exponents \eta_{L2}, \eta_{L4} and the related
anisotropy exponent \theta are fully consistent with the dimensionality
expansions to second order in \epsilon=4+m/2-d [Phys. Rev. B 62, 12338 (2000);
Nucl. Phys. B 612, 340 (2001)] inasmuch as both expansions yield the same
contributions of order \epsilon^2/n.Comment: 8 pages, submitted to J. Phys.
Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order
A two-loop renormalization group analysis of the critical behaviour at an
isotropic Lifshitz point is presented. Using dimensional regularization and
minimal subtraction of poles, we obtain the expansions of the critical
exponents and , the crossover exponent , as well as the
(related) wave-vector exponent , and the correction-to-scaling
exponent to second order in . These are compared with
the authors' recent -expansion results [{\it Phys. Rev. B} {\bf 62}
(2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of
an -axial Lifshitz point. It is shown that the expansions obtained here by a
direct calculation for the isotropic () Lifshitz point all follow from the
latter upon setting . This is so despite recent claims to the
contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated
automatically via texdra
Local scale invariance and strongly anisotropic equilibrium critical systems
A new set of infinitesimal transformations generalizing scale invariance for
strongly anisotropic critical systems is considered. It is shown that such a
generalization is possible if the anisotropy exponent \theta =2/N, with N=1,2,3
... Differential equations for the two-point function are derived and
explicitly solved for all values of N. Known special cases are conformal
invariance (N=2) and Schr\"odinger invariance (N=1). For N=4 and N=6, the
results contain as special cases the exactly known scaling forms obtained for
the spin-spin correlation function in the axial next nearest neighbor spherical
(ANNNS) model at its Lifshitz points of first and second order.Comment: 4 pages Revtex, no figures, with file multicol.sty, to appear in PR
Periodic vacuum and particles in two dimensions
Different dynamical symmetry breaking patterns are explored for the two
dimensional phi4 model with higher order derivative terms. The one-loop saddle
point expansion predicts a rather involved phase structure and a new Gaussian
critical line. This vacuum structure is corroborated by the Monte Carlo method,
as well. Analogies with the structure of solids, the density wave phases and
the effects of the quenched impurities are mentioned. The unitarity of the time
evolution operator in real time is established by means of the reflection
positivity.Comment: Final version, additional references and the proof of reflection
positivity added, 41 pages, 16 figure
Lattice models and Landau theory for type II incommensurate crystals
Ground state properties and phonon dispersion curves of a classical linear
chain model describing a crystal with an incommensurate phase are studied. This
model is the DIFFOUR (discrete frustrated phi4) model with an extra
fourth-order term added to it. The incommensurability in these models may arise
if there is frustration between nearest-neighbor and next-nearest-neighbor
interactions. We discuss the effect of the additional term on the phonon
branches and phase diagram of the DIFFOUR model. We find some features not
present in the DIFFOUR model such as the renormalization of the
nearest-neighbor coupling. Furthermore the ratio between the slopes of the soft
phonon mode in the ferroelectric and paraelectric phase can take on values
different from -2. Temperature dependences of the parameters in the model are
different above and below the paraelectric transition, in contrast with the
assumptions made in Landau theory. In the continuum limit this model reduces to
the Landau free energy expansion for type II incommensurate crystals and it can
be seen as the lowest-order generalization of the simplest Lifshitz-point
model. Part of the numerical calculations have been done by an adaption of the
Effective Potential Method, orginally used for models with nearest-neighbor
interaction, to models with also next-nearest-neighbor interactions.Comment: 33 pages, 7 figures, RevTex, submitted to Phys. Rev.
General criteria for the stability of uniaxially ordered states of Incommensurate-Commensurate Systems
Reconsidering the variational procedure for uniaxial systems modeled by
continuous free energy functionals, we derive new general conditions for
thermodynamic extrema. The utility of these conditions is briefly illustrated
on the models for the classes I and II of incommensurate-commensurate systems.Comment: 5 pages, to be published in Phys. Rev. Let
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